Solve - z - z -2- i- where z is a complex number-A- undefinedB- undefinedC- undefinedD- undefined

|z| + z = 2 + i Let z = x + iy → |z| + x + iy = 2 + i Equating imaginary part, →y = 1 Equating real part, √(x^2 + y^2) + x = 2 →√(x^2 + 1) + x = 2 →√(x^2 + 1 ...

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Standard VI

Mathematics

Writing Words in Numbers

Solve | z |+ ...

Question

Solve |z| + z = 2 + i , where z is a complex number.?

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Solution

|z| + z = 2 + i
Let z = x + iy
$\to | z | + x + i y = 2 + i$
Equating imaginary part, $\Rightarrow y = 1$
Equating real part,
$\sqrt{x^{2} + y^{2}} + x = 2 \to \sqrt{x^{2} + 1} + x = 2 \to \sqrt{x^{2} + 1} = (2 - x) \to S q u a r i n g, x^{2} + 1 = 4 + x^{2} - 4 x \to 3 - 4 x = 0 o r x = \frac{3}{4}$

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Solve |z| + z = 2 + i , where z is a complex number.?

|z| + z = 2 + i Let z = x + iy →|z|+x+iy=2+i Equating imaginary part, ⇒y=1 Equating real part, √x2+y2+x=2→√x2+1+x=2→√x2+1=(2−x)→Squaring,x2+1=4+x2−4x→3−4x=0 or x=34